arXiv research

The paper compares heat kernels on manifolds with Robin boundary conditions.

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…

The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic heat kernels, with appropriate modifications, does yield heat kernels for subell…

The paper studies heat kernel asymptotics and proves Morse inequalities.

Formulae connect heat kernels on glued manifolds.

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We show explicitly that the obtaine…

Proves upper bounds for heat kernels evolving on manifolds.

In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres. Finally, as an application, we compute the diagonal of heat kernels for odd dimensional…

From the uniformization theorem, we know that every Riemann surface has a simply-connected covering space. Moreover, there are only three simply-connected Riemann surfaces: the sphere, the Euclidean plane, and the hyperbolic plane. In this paper, we collect the known heat kernels, or Green's functions, for these three …

In a 1991 paper by Buttig and Eichhorn, the existence and uniqueness of a differential forms heat kernel on open manifolds of bounded geometry was proven. In that paper, it was shown that the heat kernel obeyed certain properties, one of which was a relationship between the derivative of heat kernel of different degree…

Heat kernel estimates on manifolds with mixed boundary conditions.

Proves heat kernel superconvexity in hyperbolic space.

Derives properties of heat kernel for Rumin complex on Heisenberg groups.

Proposes learning manifold implicitly via heat kernel.

The paper studies local heat kernel properties on smooth manifolds.

In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an estimate on Laplacian form of the heat kernel on complete manifolds with nonnegative R…

The paper studies heat kernel asymptotics for Kohn Laplacians on CR manifolds.

Heat kernel resurgent structure from Picard-Lefschetz theory

The paper develops heat kernel comparison theorems and applies them to spectral geometry.

In this paper, we study the large time behavior of the heat kernel on complete Riemannian manifolds with nonnegative Ricci curvature, which was studied by P. Li with additional maximum volume growth assumption. Following Y. Ding's original strategy, by blowing down the metric, using Cheeger and Colding's theory about l…

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…

Estimates heat kernel gradients on fractal-like cable systems.

The study examines heat kernel bounds on Riemannian manifolds with an end.

The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel formula is explicit enough to derive small time asymptotics. Related twistor spaces and corresponding heat kern…

Sharp Gaussian bounds derived for Schrödinger kernel on Ricci solitons.

Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.

Extends heat kernel estimates for super Ricci flow.

We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the heat kernel function itself. We then apply these bounds to derive an estimate on the gradient of solutions of the heat equation, which is kno…

The paper studies heat kernels on weighted Riemannian manifolds with curvature bounds.

Maps embed manifolds using heat kernels of connection Laplacian.

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of usi…

In this paper, we compute the first two equivariant heat kernel coefficients of the Bochner Laplacian on differential forms. The first two equivariant heat kernel coefficients of the Bochner Laplacian with torsion are also given. We also study the equivariant heat kernel coefficients of nonmininmal operators on differe…

Study heat kernel on quaternionic contact manifolds, finding linear dependence of coefficients on curvature.

Study subelliptic heat kernel on octonionic anti-de Sitter space.

We study the subelliptic heat kernels of the CR three dimensional solvable Lie groups. We first classify all left-invariant sub-Riemannian structures on three dimensional solvable Lie groups and obtain representations of these groups. We give expressions for the heat kernels on these groups and obtain heat semigroup gr…

Paper improves heat kernel estimates on Ricci shrinkers.

We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part $-\N^μ\N_μ$. Our objective is to obtain information on the asymptotic expansions of the corresponding r…

New example of manifolds with monotonic heat kernels found.

Uniform heat kernel and diffusion bridge asymptotics for sub-Riemannian geometry.

The paper studies heat kernels on modified manifolds and bounds their properties.

Study Brownian motions and heat kernel bounds on Kähler and quaternion Kähler manifolds.

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

We treat the Witten operator on the de Rham complex with semiclassical heat kernel methods to derive the Poincaré-Hopf theorem and degenerate generalizations of it. Thereby, we see how the semiclassical asymptotics of the Witten heat kernel are related to approaches using the Thom form of Mathai and Quillen.

We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the short-time asymptotic expansion of the heat kernel is calculated explicitly.

We give a proof of Gaussian upper bound for the heat kernel coupled with the Ricci ow. Previous proofs by Lei Ni [5] use Harnack inequality and doubling volume property, also the recent proof by Zhang and Cao [6] uses Sobolev type inequality that is conserved along Ricci ow. We will use a horizontal coupling of curve […

We study orbital functions associated to Kleinian groups through the heat kernel approach developed in \cite{artmoiheatcounting1}.

This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the $L^p$ norms of the Radon-Nikodym derivatives. We also prove that a logarithmic Sobolev inequality holds …

Let $(X,d,μ)$ be a $RCD^\ast(K, N)$ space with $K\in \mathbb{R}$ and $N\in [1,\infty]$. For $N\in [1,\infty)$, we derive the upper and lower bounds of the heat kernel on $(X,d,μ)$ by applying the parabolic Harnack inequality and the comparison principle, and then sharp bounds for its gradient, which are also sharp in t…